Old-Fashioned Parametric Models are Still the Best: A Comparison of Value-at-Risk Approaches in Several Volatility States

Numerous advances in the modelling techniques of Value-at-Risk (VaR) have provided the financial institutions with a wide scope of market risk approaches. Yet it remains unknown which of the models should be used depending on the state of volatility. In this article we present the backtesting results for 1% and 2.5% VaR of six indexes from emerging and developed countries using several most known VaR models, among many: GARCH, EVT, CAViaR and FHS with multiple sets of parameters. The backtesting procedure has been based on the excess ratio, Kupiec and Christoffersen tests for multiple thresholds and cost functions. The added value of this article is that we have compared the models in four different scenarios, with different states of volatility in training and testing samples. The results indicate that the best of the models that is the least affected by changes in the volatility is GARCH(1,1) with standardized student's t-distribution. Non-parmetric techniques (e.g. CAViaR with GARCH setup (see Engle and Manganelli, 2001) or FHS with skewed normal distribution) have very prominent results in testing periods with low volatility, but are relatively worse in the turbulent periods. We have also discussed an automatic method to setting a threshold of extreme distribution for EVT models, as well as several ensembling methods for VaR, among which minimum of best models has been proven to have very good results - in particular a minimum of GARCH(1,1) with standardized student's t-distribution and either EVT or CAViaR models.